Group #24984160 — subgroups

Subgroups — #24984160

Order 11008.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136686	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1381	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₄₄	C₄	1	1	yes	characteristic
5	#14583140	—	2	1	no	—
6	C₂×C₄₃⋊C₃₂	—	2	1	no	—
7	#14582725	C₄	1	1	yes	characteristic
8	#14582704	—	2	1	no	—
9	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×#108×C₄₃	—	2	1	no	—
11	C₂×Dic₁₇₂	—	2	1	no	—
12	#13063304	—	4	1	no	—
13	Dic₃₄₄	—	4	1	no	—
14	#13063259	—	2	1	no	—
15	#13063250	—	4	1	no	—
16	C₄₃⋊C₃₂	—	4	1	no	—
17	C₂×M₁₆×C₄₃	—	4	1	no	—
18	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	—	4	1	no	—
20	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
22	#108×C₄₃	—	2	2	no	—
23	#108×C₄₃	—	4	1	no	—
24	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
25	C₂×Dic₈₆	—	4	1	no	—
26	M₁₆×C₄₃	—	4	2	no	—
27	M₁₆×C₄₃	—	8	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	—	2	1	no	—
30	C₂×C₈×C₄₃	—	8	1	no	—
31	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
33	C₂²⋊Dic₄₃	—	8	1	no	—
34	C₄⋊Dic₄₃	—	4	1	no	—
35	Dic₄₃⋊C₄	—	8	1	no	—
36	Dic₁₇₂	—	4	1	no	—
37	Dic₁₇₂	—	4	1	no	—
38	C₁₆×C₄₃	—	2	1	no	—
39	C₁₆×C₄₃	—	2	1	no	—
40	C₂³×C₄₃	SD₃₂	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
44	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
45	C₂×Dic₄₃	—	8	1	no	—
46	C₂×Dic₄₃	—	8	1	no	—
47	Dic₈₆	—	8	1	no	—
48	Dic₈₆	—	8	1	no	—
49	C₈×C₄₃	—	2	1	no	—
50	C₈×C₄₃	—	8	2	no	—
51	C₈×C₄₃	#99	1	1	yes	characteristic
52	C₈×C₄₃	#104	1	1	yes	characteristic
53	#7421	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	1	no	—
55	C₂²×C₄₃	—	2	1	no	—
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	#357	1	1	yes	characteristic
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	#327	1	1	yes	characteristic
60	C₄×C₄₃	#360	1	1	yes	characteristic
61	Dic₄₃	—	16	1	no	—
62	Dic₄₃	—	16	1	no	—
63	#2216	—	43	1	no	—
64	C₂²⋊C₃₂	—	43	1	no	—
65	#1381	D₄₃	1	1	yes	characteristic
66	C₂×C₄₃	—	4	1	no	—
67	C₂×C₄₃	#1347	1	1	yes	characteristic
68	C₂×C₄₃	#1417	1	1	yes	characteristic
69	C₂×C₄₃	#1420	1	1	yes	characteristic
70	C₂×Q₃₂	—	43	1	no	—
71	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
72	#467	—	86	1	no	—
73	C₂×#108	—	2	1	no	—
74	C₂×C₃₂	—	86	1	no	—
75	#366	—	43	1	no	—
76	#358	—	86	1	no	—
77	C₄₃	#7421	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₁₆	—	86	1	no	—
79	C₂×M₁₆	—	4	1	no	—
80	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₂²⋊Q₈	—	172	1	no	—
82	Q₃₂	—	172	1	no	—
83	C₂×C₁₆	—	4	1	no	—
84	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
85	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
86	#108	—	2	2	no	—
87	#108	—	4	1	no	—
88	#107	—	86	1	no	—
89	#103	—	172	1	no	—
90	C₃₂	—	172	1	no	—
91	C₂×Q₈	—	172	1	no	—
92	C₂²×C₄	#10621882	1	1	yes	characteristic
93	Q₁₆	—	172	1	no	—
94	Q₁₆	—	172	1	no	—
95	M₁₆	—	4	2	no	—
96	M₁₆	—	8	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	8	1	no	—
100	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
101	C₂×C₈	#10621884	1	1	yes	characteristic
102	C₄⋊C₄	—	344	1	no	—
103	C₄⋊C₄	—	172	1	no	—
104	C₂²⋊C₄	—	344	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	2	1	no	—
107	C₂³	#13063268	1	1	yes	characteristic
108	Q₈	—	344	1	no	—
109	Q₈	—	344	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	344	1	no	—
113	C₂×C₄	—	344	1	no	—
114	C₂×C₄	#13063245	1	1	yes	characteristic
115	C₂×C₄	#13063266	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	8	2	no	—
118	C₈	#13063239	1	1	yes	characteristic
119	C₈	#13063253	1	1	yes	characteristic
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	#14582699	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	688	1	no	—
126	C₄	—	688	1	no	—
127	C₄	#14582632	1	1	yes	characteristic
128	C₄	#14582708	1	1	yes	characteristic
129	C₂	—	4	1	no	—
130	C₂	#19132603	1	1	yes	characteristic
131	C₂	#19132778	1	1	yes	characteristic
132	C₂	#19132787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136686

C₂

yes

maximal, characteristic

C₂²⋊(C₄₃⋊C₃₂)

C₂

yes

maximal, characteristic

C₄₃×#1381

C₂

yes

maximal, characteristic

C₂×Dic₃₄₄

C₄

yes

characteristic

#14583140

—

C₂×C₄₃⋊C₃₂

—

#14582725

C₄

yes

characteristic

#14582704

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

—

C₂×Dic₁₇₂

—

#13063304

—

Dic₃₄₄

—

#13063259

—

#13063250

—

C₄₃⋊C₃₂

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

#108×C₄₃

—

#108×C₄₃

—

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₂³×C₄₃

SD₃₂

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

characteristic

C₂×C₄×C₄₃

D₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#357

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2216

—

C₂²⋊C₃₂

—

#1381

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×Q₃₂

—

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

#467

—

C₂×#108

—

C₂×C₃₂

—

#366

—

#358

—

C₄₃

#7421

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

C₂²⋊Q₈

—

172

—

Q₃₂

—

172

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₄₃

yes

characteristic

C₂×C₁₆

D₁₇₂

yes

—

—

—

—

172

—

C₃₂

—

172

—

C₂×Q₈

—

172

—

C₂²×C₄

#10621882

yes

characteristic

Q₁₆

—

172

—

Q₁₆

—

172

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

101

C₂×C₈

#10621884

yes

characteristic

102

C₄⋊C₄

—

344

—

103

C₄⋊C₄

—

172

—

104

C₂²⋊C₄

—

344

—

105

C₁₆

—

106

C₁₆

—

107

C₂³

#13063268

yes

characteristic

108

Q₈

—

344

—

109

Q₈

—

344

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

344

—

113

C₂×C₄

—

344

—

114

C₂×C₄

#13063245

yes

characteristic

115

C₂×C₄

#13063266

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

#13063239

yes

characteristic

119

C₈

#13063253

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#14582699

yes

characteristic

124

C₄

—

125

C₄

—

688

—

126

C₄

—

688

—

127

C₄

#14582632

yes

characteristic

128

C₄

#14582708

yes

characteristic

129

C₂

—

130

C₂

#19132603

yes

characteristic

131

C₂

#19132778

yes

characteristic

132

C₂

#19132787

yes

characteristic

	subgroup	G/H
center	C₂²	#14582699
commutator	C₂×C₁₆×C₄₃	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1381	C₂
socle	C₂²×C₄₃	#357
prime radical	C₂³×C₄₃	SD₃₂
cosocle	C₂²×C₁₆×C₄₃	C₂²
hypercenter	#1381	D₄₃
hypocenter	C₄₃	#7421
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #1381

subgroup

G/H

center

C₂²

#14582699

commutator

C₂×C₁₆×C₄₃

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₄₃

Fitting

C₄₃×#1381

C₂

socle

C₂²×C₄₃

#357

prime radical

C₂³×C₄₃

SD₃₂

cosocle

C₂²×C₁₆×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #1381

N	H ≅ G/N	type
77. C₄₃	#7421	semidirect

H ≅ G/N

type

77. C₄₃

#7421

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19136686	2
C₂²⋊(C₄₃⋊C₃₂)	2
C₄₃×#1381	2
#7421	43

subgroup

index

#19136686

C₂²⋊(C₄₃⋊C₃₂)

C₄₃×#1381

#7421

Subgroups — #24984160

Conjugacy classes of subgroups

Complements

Maximal subgroups